Most of the conventional floating mobile objects (such as airplanes, helicopters, and submersibles) that are operated in the air or under water are underactuated systems with the range in which the total thrust vector obtained by combining all vectors of the thrust generated by thrusters can be generated is less than six dimensions, and such a conventional floating mobile object is equipped with a rudder for allowing movement in a six-dimensional space. Such a floating mobile object that is not holonomic (referred to below as a nonholonomic floating mobile object) is not required to generate thrust in every direction of the six-dimensional space, and therefore, the thrust efficiency of the thruster is high. This is advantageous particularly under gravity, in which upward force is always required for floating. However, such a nonholonomic floating mobile object has issues in that its frame structure and control law are complicated.
More specifically, since the nonholonomic floating mobile object is provided with a rudder, mechanisms for moving and controlling the rudder are required, resulting in a complicated frame structure. This is problematic particularly to relatively small-sized floating mobile objects.
Furthermore, Brockett's theorem suggests that the nonholonomic system is not capable of achieving asymptotic stability to an equilibrium point by a smooth time-invariant feedback control law (see Non-Patent Document 1), and therefore, it can be appreciated that the nonholonomic floating mobile object cannot be controlled stably by, for example, a simple PD control law alone. Accordingly, the nonholonomic floating mobile object requires, for example, hierarchization and switching of control laws.
For example, a helicopter or a quadrotor can generate thrust only upward but not laterally when the fuselage is hovering horizontally. Accordingly, in the case where a helicopter or a quadrotor moves horizontally from the state of hovering, it is necessary to take a plurality of steps of, in response to a single command to move horizontally, inclining the fuselage (or a propeller(s)) and thereafter generating horizontal thrust. Furthermore, in the case where the fuselage is in a crosswind during horizontal hovering, to continue the hovering in a fixed position, it is necessary, as in the above, to take a plurality of steps of inclining the fuselage (or a propeller(s)) and thereafter generating horizontal thrust, which results in a late response to crosswind. Therefore, the control law for the nonholonomic floating mobile object becomes complicated, and further, if there is disturbance such as wind, control performance is reduced.
Accordingly, to solve the issues with the nonholonomic floating mobile object, floating mobile objects that are holonomic (referred to below as holonomic floating mobile objects) have been proposed (see, for example, Non-Patent Document 2 and Patent Documents 1 and 2).
Non-Patent Document 2 discloses an ODIN (Omni-Directional Intelligent Navigator), which is a holonomic floating mobile object including eight thrusters controlled independently of one another. Patent Document 1 discloses a holonomic floating mobile object which includes six thrusters controlled independently of one another and generating thrust in different directions from one another. All of these holonomic floating mobile objects are used under water where the effect of gravity is cancelled out by flotation, and therefore, low thrust efficiency of the thruster, which is a disadvantage of the holonomic system, is negligible. Accordingly, the holonomic floating mobile objects can apply high control performance, which is an advantage of the holonomic system.
Patent Document 2 discloses a hybrid airship, which is a holonomic floating mobile object including a balloon and a plurality of thrusters controlled independently of one another. In this hybrid airship, the effect of gravity is cancelled out by flotation of the balloon, and therefore, as in the case of the holonomic floating mobile objects that are used under water, low thrust efficiency of the thruster, which is a disadvantage of the holonomic system, is negligible. Accordingly, the hybrid airship can also apply high control performance, which is an advantage of the holonomic system.